We model a Systemically Important Financial Institution (SIFI) that is too big(or too interconnected) to fail. Without credible regulation and strong supervision,the shareholders of this institution might deliberately let its managers take excessiverisk. We propose a solution to this problem, showing how insurance againstsystemic shocks can be provided without generating moral hazard. The solutioninvolves levying a systemic tax needed to cover the costs of future crises and moreimportantly establishing a Systemic Risk Authority endowed with special resolutionpowers, including the control of bankers' compensation packages during crisisperiods.